an:06496848
Zbl 1327.90144
Wei, Zhou; Ali, M. Montaz
Convex mixed integer nonlinear programming problems and an outer approximation algorithm
EN
J. Glob. Optim. 63, No. 2, 213-227 (2015).
0925-5001 1573-2916
2015
j
90C11 90C25 90C30
convex MINLP; outer approximation; decomposition; master program
Summary: In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one.